Systems and methods for parameter adaptation

Abstract

A method of parameter adaptation is used to modify the parameters of a model to improve model performance. The model separately estimates the contribution of each model parameter to the prediction error. It achieves this by transforming to the time-scale plane the vectors of output sensitivities with respect to model parameters and then identifying the regions within the time-scale plane at which the dynamic effect of individual model parameters is dominant on the output. The method then attributes the prediction error in these regions to the deviation of a single parameter from its true value as the basis of estimating individual parametric errors. The proposed Signature Isolation Method (PARSIM) then uses these estimates to adapt individual model parameters independently of the others, implementing, in effect, concurrent adaptation of individual parameters by the Newton-Raphson method in the time-scale plane. The Signature Isolation Method has been found to have an adaptation precision comparable to that of the Gauss-Newton method for noise-free cases. However, it surpasses the Gauss-Newton method in precision when the output is contaminated with noise or when the measurements are generated by inadequate excitation.

Description

CROSS REFERENCE TO RELATED APPLICATION[0001]This application is a continuation-in-part application of U.S. application Ser. No. 12 / 220,446, filed on Jul. 24, 2008, and also claims priority to U.S. Application No. 61 / 250,349, filed on Oct. 9, 2009, the entire contents of the above applications being incorporated herein by reference.BACKGROUND OF THE INVENTION[0002]Engineers and scientists are increasingly turning to sophisticated computer-based simulation models to predict and optimize process behavior in virtual environments. Yet, to be effective, simulation models need to have a high degree of accuracy to be reliable. An important part of simulation development, therefore, is parameter adaptation wherein the values of model parameters (i.e., model coefficients and exponents) are adjusted so as to maximize the accuracy of simulation relative to the experimental data available from the process. If parameter adaptation leads to acceptable predictions, the model is declared valid. Othe...

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Benefits of technology

[0007]A preferred embodiment uses a transformation that identifies regions of the time-scale plane at which the effect of each parameter on the prediction error is dominant. It then approximates the prediction error in each region in terms of a single parameter to estimate the corresponding parameter's deviation from its “true” value, i.e., the parameter value that can be used to more accurately represent or model a selected system or method. Using these estimates, it then adapts individual parameters independently of the others in direct contrast to traditional error minimization of regression. This process can be referred to as the Parameter Signature Isolation Method (PARSIM), which takes the form of the Newton-Raphson method applied to single-parameter models, has been shown to provide better precision than the Gauss-Newton method in presence of noise. PARSIM is also found to produce more consistent and precise estimates of the parameters in the absence of rich excitation.

[0008]A preferred embodiment of the invention uses a processing system to perform the transformation and determine parameter values. The processing system can be a computer programmed to perform parameter adaptation for a variety of different applications. The system performs a process sequence in accordance with a programmed set of instructions that includes transformation to a selected domain and minimization of error associated with a given parameter value.

[0010]Preferred embodiments of the present invention can be used in diverse applications including the design and use of engines such as gas turbine engines that can be used to propel aircraft and other vehicles. These systems can also be used in the design and use of control systems, such as building HVAC systems, chemical plant operations, in fault diagnosis and other simulation applications. A model based recurrent neural network can also be analyzed using the systems and methods described herein the neural network nodes can be represented by contours of Gaussian radial basis function (RBF) where the system is drained by adjusting the weights of the RBFs to modify the contours of the activation functions. The systems and methods can also be used in the design and use of filters or filter banks, which can be used in noise suppression, for example. This can be done, for example, by transforming the signal to the time scale domain, reducing the high frequency noise by thresholding the wavelength coefficients in the lower scales (higher frequencies) but avoids the need to reconstruct wavelet coefficients in the time domain due to the determination of parameters in the time-scale domain.

Problems solved by technology

However, not all model parameters are erroneous.

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